%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRA004+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:23:34 PM UTC 2026
% Result : Theorem 4.42s 1.31s
% Output : CNFRefutation 4.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 7
% Syntax : Number of formulae : 104 ( 15 unt; 0 def)
% Number of atoms : 465 ( 155 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 584 ( 223 ~; 260 |; 87 &)
% ( 3 <=>; 9 =>; 0 <=; 2 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 299 ( 0 sgn 275 !; 24 ?; 124 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1,X2,X3] :
( ( on_path(X3,X2)
& path(X0,X1,X2) )
=> ( in_path(tail_of(X3),X2)
& in_path(head_of(X3),X2)
& edge(X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',on_path_properties) ).
fof(f8,axiom,
! [X0,X1] :
( sequential(X0,X1)
<=> ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',sequential_defn) ).
fof(f9,axiom,
! [X0,X1,X2] :
( path(X1,X2,X0)
=> ! [X3,X4] :
( ( ( ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) )
| sequential(X3,X4) )
& on_path(X4,X0)
& on_path(X3,X0) )
=> precedes(X3,X4,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',precedes_defn) ).
fof(f10,axiom,
! [X0,X1,X2] :
( path(X1,X2,X0)
=> ! [X3,X4] :
( precedes(X3,X4,X0)
=> ( ( sequential(X3,X4)
<~> ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',precedes_properties) ).
fof(f11,axiom,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( ! [X3] :
( path(X0,X1,X3)
=> less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1
& path(X0,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',shortest_path_defn) ).
fof(f12,axiom,
! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( ~ precedes(X3,X2,X4)
& ~ ? [X5] :
( head_of(X5) = head_of(X3)
& tail_of(X5) = tail_of(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',shortest_path_properties) ).
fof(f18,conjecture,
! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( head_of(X3) != head_of(X2)
& head_of(X3) != tail_of(X2)
& ~ ? [X5] :
( head_of(X5) = head_of(X3)
& tail_of(X5) = tail_of(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_properties_lemma) ).
fof(f19,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( head_of(X3) != head_of(X2)
& head_of(X3) != tail_of(X2)
& ~ ? [X5] :
( head_of(X5) = head_of(X3)
& tail_of(X5) = tail_of(X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( ~ on_path(X3,X2)
| ~ path(X0,X1,X2)
| ( in_path(tail_of(X3),X2)
& in_path(head_of(X3),X2)
& edge(X3) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( ~ on_path(X3,X2)
| ~ path(X0,X1,X2)
| ( in_path(tail_of(X3),X2)
& in_path(head_of(X3),X2)
& edge(X3) ) ),
inference(flattening,[],[f27]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ! [X3,X4] :
( ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
& ~ sequential(X3,X4) )
| ~ on_path(X4,X0)
| ~ on_path(X3,X0)
| precedes(X3,X4,X0) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ! [X3,X4] :
( ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
& ~ sequential(X3,X4) )
| ~ on_path(X4,X0)
| ~ on_path(X3,X0)
| precedes(X3,X4,X0) ) ),
inference(flattening,[],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ! [X3,X4] :
( ~ precedes(X3,X4,X0)
| ( ( sequential(X3,X4)
<~> ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f34,plain,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( ! [X3] :
( ~ path(X0,X1,X3)
| less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1
& path(X0,X1,X2) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f35,plain,
! [X0,X1,X2,X3,X4] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| ( ~ precedes(X3,X2,X4)
& ! [X5] :
( head_of(X3) != head_of(X5)
| tail_of(X2) != tail_of(X5) ) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f36,plain,
! [X0,X1,X2,X3,X4] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| ( ~ precedes(X3,X2,X4)
& ! [X5] :
( head_of(X3) != head_of(X5)
| tail_of(X2) != tail_of(X5) ) ) ),
inference(flattening,[],[f35]) ).
fof(f43,plain,
? [X0,X1,X2,X3,X4] :
( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4)
& ( head_of(X2) = head_of(X3)
| tail_of(X2) = head_of(X3)
| ? [X5] :
( head_of(X5) = head_of(X3)
& tail_of(X5) = tail_of(X2) ) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f44,plain,
? [X0,X1,X2,X3,X4] :
( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4)
& ( head_of(X2) = head_of(X3)
| tail_of(X2) = head_of(X3)
| ? [X5] :
( head_of(X5) = head_of(X3)
& tail_of(X5) = tail_of(X2) ) ) ),
inference(flattening,[],[f43]) ).
fof(f50,plain,
! [X0,X1] :
( ( ~ sequential(X0,X1)
| ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) ) )
& ( head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0)
| sequential(X0,X1) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f51,plain,
! [X0,X1] :
( ( ~ sequential(X0,X1)
| ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) ) )
& ( head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0)
| sequential(X0,X1) ) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ! [X3,X4] :
( ~ precedes(X3,X4,X0)
| ( ( sequential(X3,X4)
| ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) ) )
& ( ~ sequential(X3,X4)
| ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ! [X3,X4] :
( ~ precedes(X3,X4,X0)
| ( ( sequential(X3,X4)
| ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) ) )
& ( ~ sequential(X3,X4)
| ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ! [X3,X4] :
( ~ precedes(X3,X4,X0)
| ( ( sequential(X3,X4)
| ? [X6] :
( precedes(X6,X4,X0)
& sequential(X3,X6) ) )
& ( ~ sequential(X3,X4)
| ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
inference(rectify,[],[f53]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ! [X3,X4] :
( ~ precedes(X3,X4,X0)
| ( ( sequential(X3,X4)
| ( precedes(sK3(X0,X3,X4),X4,X0)
& sequential(X3,sK3(X0,X3,X4)) ) )
& ( ~ sequential(X3,X4)
| ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X6,sK3(X0,X3,X4))],[f54]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ( ~ shortest_path(X0,X1,X2)
| ( ! [X3] :
( ~ path(X0,X1,X3)
| less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1
& path(X0,X1,X2) ) )
& ( ? [X3] :
( path(X0,X1,X3)
& ~ less_or_equal(length_of(X2),length_of(X3)) )
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ( ~ shortest_path(X0,X1,X2)
| ( ! [X3] :
( ~ path(X0,X1,X3)
| less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1
& path(X0,X1,X2) ) )
& ( ? [X3] :
( path(X0,X1,X3)
& ~ less_or_equal(length_of(X2),length_of(X3)) )
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ( ~ shortest_path(X0,X1,X2)
| ( ! [X4] :
( ~ path(X0,X1,X4)
| less_or_equal(length_of(X2),length_of(X4)) )
& X0 != X1
& path(X0,X1,X2) ) )
& ( ? [X3] :
( path(X0,X1,X3)
& ~ less_or_equal(length_of(X2),length_of(X3)) )
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ) ),
inference(rectify,[],[f57]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ( ~ shortest_path(X0,X1,X2)
| ( ! [X4] :
( ~ path(X0,X1,X4)
| less_or_equal(length_of(X2),length_of(X4)) )
& X0 != X1
& path(X0,X1,X2) ) )
& ( ( path(X0,X1,sK4(X0,X1,X2))
& ~ less_or_equal(length_of(X2),length_of(sK4(X0,X1,X2))) )
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f58]) ).
fof(f61,plain,
( precedes(sK9,sK10,sK11)
& shortest_path(sK7,sK8,sK11)
& ( head_of(sK10) = head_of(sK9)
| tail_of(sK9) = head_of(sK10)
| ( head_of(sK10) = head_of(sK12)
& tail_of(sK9) = tail_of(sK12) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11,sK12]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9),skolemize(X3,sK10),skolemize(X4,sK11),skolemize(X5,sK12)],[f44]) ).
fof(f78,plain,
! [X2,X3,X0,X1] :
( ~ on_path(X3,X2)
| ~ path(X0,X1,X2)
| edge(X3) ),
inference(cnf_transformation,[],[f28]) ).
fof(f86,plain,
! [X0,X1] :
( head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0)
| sequential(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f87,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ path(X1,X2,X0)
| ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0)
| precedes(X3,X4,X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f92,plain,
! [X2,X3,X0,X1,X4] :
( ~ path(X1,X2,X0)
| ~ precedes(X3,X4,X0)
| on_path(X4,X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f93,plain,
! [X2,X3,X0,X1,X4] :
( ~ path(X1,X2,X0)
| ~ precedes(X3,X4,X0)
| on_path(X3,X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f96,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f59]) ).
fof(f100,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| head_of(X3) != head_of(X5)
| tail_of(X2) != tail_of(X5) ),
inference(cnf_transformation,[],[f36]) ).
fof(f109,plain,
precedes(sK9,sK10,sK11),
inference(cnf_transformation,[],[f61]) ).
fof(f110,plain,
shortest_path(sK7,sK8,sK11),
inference(cnf_transformation,[],[f61]) ).
fof(f111,plain,
( head_of(sK10) = head_of(sK9)
| tail_of(sK9) = head_of(sK10)
| head_of(sK10) = head_of(sK12) ),
inference(cnf_transformation,[],[f61]) ).
fof(f112,plain,
( head_of(sK10) = head_of(sK9)
| tail_of(sK9) = head_of(sK10)
| tail_of(sK9) = tail_of(sK12) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( edge(X3)
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( X0 = X1 )
| ~ edge(X1)
| ~ edge(X0)
| ( head_of(X0) != tail_of(X1) ) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( precedes(X5,X4,X2)
| ~ sequential(X5,X3)
| ~ on_path(X5,X2)
| ~ on_path(X4,X2)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( on_path(X3,X2)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( on_path(X4,X2)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i] :
( path(X0,X1,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ shortest_path(X4,X5,X3)
| ~ precedes(X2,X0,X3)
| ( tail_of(X1) != tail_of(X2) )
| ( head_of(X0) != head_of(X1) ) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_96,negated_conjecture,
( ( tail_of(sK9) = tail_of(sK12) )
| ( head_of(sK10) = tail_of(sK9) )
| ( head_of(sK9) = head_of(sK10) ) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_97,negated_conjecture,
( ( head_of(sK10) = tail_of(sK9) )
| ( head_of(sK12) = head_of(sK10) )
| ( head_of(sK9) = head_of(sK10) ) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_98,negated_conjecture,
shortest_path(sK7,sK8,sK11),
inference(cnf_transformation,[],[f110]) ).
tcf(c_99,negated_conjecture,
precedes(sK9,sK10,sK11),
inference(cnf_transformation,[],[f109]) ).
tcf(c_137,plain,
path(sK7,sK8,sK11),
inference(superposition,[status(thm)],[c_98,c_83]) ).
tcf(c_190,plain,
! [X0: $i] :
( sequential(X0,sK9)
| ( X0 = sK9 )
| ( head_of(sK12) = head_of(sK10) )
| ( head_of(sK9) = head_of(sK10) )
| ~ edge(sK9)
| ~ edge(X0)
| ( head_of(X0) != head_of(sK10) ) ),
inference(superposition,[status(thm)],[c_97,c_69]) ).
tcf(c_221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ shortest_path(X3,X4,X2)
| ~ precedes(X1,X0,X2)
| ( tail_of(X0) != tail_of(X1) ) ),
inference(equality_resolution,[status(thm)],[c_86]) ).
tcf(c_222,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( precedes(X5,X4,X2)
| ~ sequential(X5,X3)
| ~ on_path(X5,X2)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,X2) ),
inference(global_subsumption_just,[status(thm)],[c_75,c_77,c_75]) ).
tcf(c_223,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( precedes(X5,X4,X2)
| ~ sequential(X5,X3)
| ~ on_path(X5,X2)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_222]) ).
tcf(c_234,plain,
! [X0: $i,X1: $i,X2: $i] :
( precedes(X2,X1,sK11)
| ~ on_path(X2,sK11)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK11) ),
inference(superposition,[status(thm)],[c_137,c_223]) ).
tcf(c_238,plain,
! [X0: $i,X1: $i] :
( on_path(X1,sK11)
| ~ precedes(X0,X1,sK11) ),
inference(superposition,[status(thm)],[c_137,c_77]) ).
tcf(c_284,plain,
( sequential(sK10,sK9)
| ( sK9 = sK10 )
| ( head_of(sK12) = head_of(sK10) )
| ( head_of(sK9) = head_of(sK10) )
| ~ edge(sK10)
| ~ edge(sK9) ),
inference(equality_resolution,[status(thm)],[c_190]) ).
tcf(c_293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK12) = head_of(sK10) )
| ( head_of(sK9) = head_of(sK10) )
| ~ precedes(sK9,X0,X3)
| ~ shortest_path(X1,X2,X3)
| ( tail_of(X0) != head_of(sK10) ) ),
inference(superposition,[status(thm)],[c_97,c_221]) ).
tcf(c_295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,X0,X1) ),
inference(equality_resolution,[status(thm)],[c_221]) ).
tcf(c_307,plain,
on_path(sK10,sK11),
inference(superposition,[status(thm)],[c_99,c_238]) ).
tcf(c_384,plain,
! [X0: $i] :
( precedes(X0,sK10,sK11)
| ~ sequential(X0,sK9)
| ~ on_path(X0,sK11) ),
inference(superposition,[status(thm)],[c_99,c_234]) ).
tcf(c_386,plain,
( precedes(sK10,sK10,sK11)
| ~ sequential(sK10,sK9)
| ~ on_path(sK10,sK11) ),
inference(instantiation,[status(thm)],[c_384]) ).
tcf(c_435,plain,
! [X0: $i] : ~ precedes(X0,X0,sK11),
inference(superposition,[status(thm)],[c_98,c_295]) ).
tcf(c_436,plain,
~ precedes(sK10,sK10,sK11),
inference(instantiation,[status(thm)],[c_435]) ).
tcf(c_481,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK12) = head_of(sK10) )
| ( head_of(sK9) = head_of(sK10) )
| ~ precedes(sK9,sK9,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_97,c_293]) ).
tcf(c_656,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ precedes(sK9,sK9,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_481,c_295,c_295]) ).
tcf(c_663,plain,
~ precedes(sK9,sK9,sK11),
inference(superposition,[status(thm)],[c_98,c_656]) ).
tcf(c_902,plain,
path(sK7,sK8,sK11),
inference(superposition,[status(thm)],[c_98,c_83]) ).
tcf(c_960,plain,
! [X0: $i] :
( sequential(X0,sK9)
| ( X0 = sK9 )
| ( head_of(sK12) = head_of(sK10) )
| ( head_of(sK9) = head_of(sK10) )
| ~ edge(sK9)
| ~ edge(X0)
| ( head_of(X0) != head_of(sK10) ) ),
inference(superposition,[status(thm)],[c_97,c_69]) ).
tcf(c_1006,plain,
! [X0: $i,X1: $i] :
( on_path(X0,sK11)
| ~ precedes(X0,X1,sK11) ),
inference(superposition,[status(thm)],[c_902,c_76]) ).
tcf(c_1008,plain,
! [X0: $i] :
( edge(X0)
| ~ on_path(X0,sK11) ),
inference(superposition,[status(thm)],[c_902,c_63]) ).
tcf(c_1009,plain,
( edge(sK10)
| ~ on_path(sK10,sK11) ),
inference(instantiation,[status(thm)],[c_1008]) ).
tcf(c_1052,plain,
( sequential(sK10,sK9)
| ( sK9 = sK10 )
| ( head_of(sK12) = head_of(sK10) )
| ( head_of(sK9) = head_of(sK10) )
| ~ edge(sK10)
| ~ edge(sK9) ),
inference(equality_resolution,[status(thm)],[c_960]) ).
tcf(c_1084,plain,
on_path(sK9,sK11),
inference(superposition,[status(thm)],[c_99,c_1006]) ).
tcf(c_1172,plain,
( ~ edge(sK9)
| ( head_of(sK9) = head_of(sK10) )
| ( head_of(sK12) = head_of(sK10) )
| ( sK9 = sK10 ) ),
inference(global_subsumption_just,[status(thm)],[c_1052,c_284,c_307,c_386,c_436,c_1009]) ).
tcf(c_1173,plain,
( ( sK9 = sK10 )
| ( head_of(sK12) = head_of(sK10) )
| ( head_of(sK9) = head_of(sK10) )
| ~ edge(sK9) ),
inference(renaming,[status(thm)],[c_1172]) ).
tcf(c_1285,plain,
edge(sK9),
inference(superposition,[status(thm)],[c_1084,c_1008]) ).
tcf(c_1286,plain,
( ( sK9 = sK10 )
| ( head_of(sK12) = head_of(sK10) )
| ( head_of(sK9) = head_of(sK10) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1173,c_1285]) ).
tcf(c_1451,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK9 = sK10 )
| ( head_of(sK9) = head_of(sK10) )
| ~ precedes(X1,sK10,X4)
| ~ shortest_path(X2,X3,X4)
| ( tail_of(X0) != tail_of(X1) )
| ( head_of(X0) != head_of(sK12) ) ),
inference(superposition,[status(thm)],[c_1286,c_86]) ).
tcf(c_1634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK9 = sK10 )
| ( head_of(sK10) = tail_of(sK9) )
| ( head_of(sK9) = head_of(sK10) )
| ~ precedes(X0,sK10,X3)
| ~ shortest_path(X1,X2,X3)
| ( head_of(sK12) != head_of(sK12) )
| ( tail_of(X0) != tail_of(sK9) ) ),
inference(superposition,[status(thm)],[c_96,c_1451]) ).
tcf(c_1638,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK9 = sK10 )
| ( head_of(sK10) = tail_of(sK9) )
| ( head_of(sK9) = head_of(sK10) )
| ~ precedes(X0,sK10,X3)
| ~ shortest_path(X1,X2,X3)
| ( tail_of(X0) != tail_of(sK9) ) ),
inference(equality_resolution_simp,[status(thm)],[c_1634]) ).
tcf(c_1768,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK9 = sK10 )
| ( head_of(sK10) = tail_of(sK9) )
| ( head_of(sK9) = head_of(sK10) )
| ~ precedes(sK12,sK10,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_96,c_1638]) ).
tcf(c_1770,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK9 = sK10 )
| ( head_of(sK10) = tail_of(sK9) )
| ( head_of(sK9) = head_of(sK10) )
| ~ precedes(sK9,sK10,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(equality_resolution,[status(thm)],[c_1638]) ).
tcf(c_1839,plain,
( ( sK9 = sK10 )
| ( head_of(sK10) = tail_of(sK9) )
| ( head_of(sK9) = head_of(sK10) )
| ~ precedes(sK9,sK10,sK11) ),
inference(superposition,[status(thm)],[c_98,c_1770]) ).
tcf(c_1840,plain,
( ( sK9 = sK10 )
| ( head_of(sK10) = tail_of(sK9) )
| ( head_of(sK9) = head_of(sK10) ) ),
inference(global_subsumption_just,[status(thm)],[c_1768,c_99,c_1839]) ).
tcf(c_1853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK9 = sK10 )
| ( head_of(sK9) = head_of(sK10) )
| ~ precedes(sK9,sK10,X3)
| ~ shortest_path(X1,X2,X3)
| ( tail_of(X0) != head_of(sK10) )
| ( head_of(X0) != head_of(sK12) ) ),
inference(superposition,[status(thm)],[c_1840,c_1451]) ).
tcf(c_1855,plain,
! [X0: $i] :
( sequential(X0,sK9)
| ( sK9 = sK10 )
| ( X0 = sK9 )
| ( head_of(sK9) = head_of(sK10) )
| ~ edge(sK9)
| ~ edge(X0)
| ( head_of(X0) != head_of(sK10) ) ),
inference(superposition,[status(thm)],[c_1840,c_69]) ).
tcf(c_1916,plain,
! [X0: $i] :
( sequential(X0,sK9)
| ( sK9 = sK10 )
| ( X0 = sK9 )
| ( head_of(sK9) = head_of(sK10) )
| ( head_of(X0) != head_of(sK10) )
| ~ edge(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1855,c_1285,c_1855]) ).
tcf(c_1917,plain,
! [X0: $i] :
( sequential(X0,sK9)
| ( sK9 = sK10 )
| ( X0 = sK9 )
| ( head_of(sK9) = head_of(sK10) )
| ~ edge(X0)
| ( head_of(X0) != head_of(sK10) ) ),
inference(renaming,[status(thm)],[c_1916]) ).
tcf(c_1932,plain,
( sequential(sK10,sK9)
| ( sK9 = sK10 )
| ( head_of(sK9) = head_of(sK10) )
| ~ edge(sK10) ),
inference(equality_resolution,[status(thm)],[c_1917]) ).
tcf(c_1939,plain,
( ( sK9 = sK10 )
| ( head_of(sK9) = head_of(sK10) ) ),
inference(global_subsumption_just,[status(thm)],[c_1853,c_307,c_386,c_436,c_1009,c_1932]) ).
tcf(c_1945,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK9 = sK10 )
| ~ precedes(X1,sK10,X4)
| ~ shortest_path(X2,X3,X4)
| ( tail_of(X0) != tail_of(X1) )
| ( head_of(X0) != head_of(sK9) ) ),
inference(superposition,[status(thm)],[c_1939,c_86]) ).
tcf(c_1946,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK9 = sK10 )
| ~ shortest_path(X3,X4,X2)
| ~ precedes(X1,X0,X2)
| ( tail_of(X1) != tail_of(sK10) )
| ( head_of(X0) != head_of(sK9) ) ),
inference(superposition,[status(thm)],[c_1939,c_86]) ).
tcf(c_1973,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK9 = sK10 )
| ~ precedes(sK10,X0,X3)
| ~ shortest_path(X1,X2,X3)
| ( head_of(X0) != head_of(sK9) ) ),
inference(equality_resolution,[status(thm)],[c_1946]) ).
tcf(c_1988,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK9 = sK10 )
| ~ precedes(X0,sK10,X3)
| ~ shortest_path(X1,X2,X3)
| ( head_of(X0) != head_of(sK9) ) ),
inference(equality_resolution,[status(thm)],[c_1945]) ).
tcf(c_2001,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK9 = sK10 )
| ~ precedes(sK10,sK9,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(equality_resolution,[status(thm)],[c_1973]) ).
tcf(c_2011,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK9 = sK10 )
| ~ precedes(sK9,sK10,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(equality_resolution,[status(thm)],[c_1988]) ).
tcf(c_2026,plain,
( ( sK9 = sK10 )
| ~ precedes(sK10,sK9,sK11) ),
inference(superposition,[status(thm)],[c_98,c_2001]) ).
tcf(c_2033,plain,
( ( sK9 = sK10 )
| ~ precedes(sK9,sK10,sK11) ),
inference(superposition,[status(thm)],[c_98,c_2011]) ).
tcf(c_2034,plain,
sK9 = sK10,
inference(global_subsumption_just,[status(thm)],[c_2026,c_99,c_2033]) ).
tcf(c_2046,plain,
precedes(sK9,sK9,sK11),
inference(superposition,[status(thm)],[c_2034,c_99]) ).
tcf(c_2047,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2046,c_663]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA004+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 12:42:58 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.41 Running first-order theorem proving
% 0.16/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42
% 0.16/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.42
% 0.16/0.42 % Detected problem language: tptp
% 0.16/0.43 % Proving...
% 4.42/1.31 % SZS status Started for theBenchmark.p
% 4.42/1.31 % SZS status Theorem for theBenchmark.p
% 4.42/1.31
% 4.42/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.42/1.31
% 4.42/1.31 % ------ iProver source info
% 4.42/1.31
% 4.42/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 4.42/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.42/1.31 % git: non_committed_changes: false
% 4.42/1.31
% 4.42/1.31 % ------ Parsing...
% 4.42/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.42/1.31 % ------ Proving...
% 4.42/1.31 % ------ Problem Properties
% 4.42/1.31
% 4.42/1.31 %
% 4.42/1.31 % clauses 51
% 4.42/1.31 % conjectures 4
% 4.42/1.31 % EPR 18
% 4.42/1.31 % Horn 36
% 4.42/1.31 % unary 5
% 4.42/1.31 % binary 13
% 4.42/1.31 % lits 154
% 4.42/1.31 % lits eq 32
% 4.42/1.31 % fd_pure 0
% 4.42/1.31 % fd_pseudo 0
% 4.42/1.31 % fd_cond 0
% 4.42/1.31 % fd_pseudo_cond 3
% 4.42/1.31 % AC symbols 0
% 4.42/1.31
% 4.42/1.31 % ------ Input Options Time Limit: Unbounded
% 4.42/1.31
% 4.42/1.31
% 4.42/1.31 % ------
% 4.42/1.31 % Current options:
% 4.42/1.31 % ------
% 4.42/1.31
% 4.42/1.31
% 4.42/1.31 %
% 4.42/1.31
% 4.42/1.31 % ------ Proving...
% 4.42/1.31 %
% 4.42/1.31
% 4.42/1.31 % ------ Proving...
% 4.42/1.31 %
% 4.42/1.31
% 4.42/1.31 % SZS status Theorem for theBenchmark.p
% 4.42/1.31
% 4.42/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.42/1.32
% 4.42/1.32
%------------------------------------------------------------------------------